CA1160352A - Equipment to correct aberrations of a cathode-ray beam - Google Patents
Equipment to correct aberrations of a cathode-ray beamInfo
- Publication number
- CA1160352A CA1160352A CA000364796A CA364796A CA1160352A CA 1160352 A CA1160352 A CA 1160352A CA 000364796 A CA000364796 A CA 000364796A CA 364796 A CA364796 A CA 364796A CA 1160352 A CA1160352 A CA 1160352A
- Authority
- CA
- Canada
- Prior art keywords
- adder
- digital
- store
- register
- correction
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired
Links
Classifications
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
- H04N17/00—Diagnosis, testing or measuring for television systems or their details
- H04N17/04—Diagnosis, testing or measuring for television systems or their details for receivers
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
- H04N9/00—Details of colour television systems
- H04N9/12—Picture reproducers
- H04N9/16—Picture reproducers using cathode ray tubes
- H04N9/28—Arrangements for convergence or focusing
Landscapes
- Engineering & Computer Science (AREA)
- Multimedia (AREA)
- Signal Processing (AREA)
- Health & Medical Sciences (AREA)
- Biomedical Technology (AREA)
- General Health & Medical Sciences (AREA)
- Video Image Reproduction Devices For Color Tv Systems (AREA)
- Controls And Circuits For Display Device (AREA)
- Details Of Television Scanning (AREA)
Abstract
EQUIPMENT TO CORRECT ABERRATIONS OF A CATHODE-RAY BEAM
ABSTRACT
Aberrations of an electron beam are corrected as the beam is scanned across the screen of a cathode-ray tube by deriving correction signals from stored digital values by means of the calculus of finite differences. The digital values, which are the initial differences of polynomial correction functions, are held in store 10 and summed in adder 20, the results being converted by digital-to-analogue converter 50 to analogue signals and supplied to the cathode-ray tube. Provision is made for the reduction of error in the calculations by shifting higher order differences relative to lower order differences before addition. The circuitry may be implemented on a single chip. Preferably the invent-tion is applied to the correction of misconvergence in a shadow mask tube.
ABSTRACT
Aberrations of an electron beam are corrected as the beam is scanned across the screen of a cathode-ray tube by deriving correction signals from stored digital values by means of the calculus of finite differences. The digital values, which are the initial differences of polynomial correction functions, are held in store 10 and summed in adder 20, the results being converted by digital-to-analogue converter 50 to analogue signals and supplied to the cathode-ray tube. Provision is made for the reduction of error in the calculations by shifting higher order differences relative to lower order differences before addition. The circuitry may be implemented on a single chip. Preferably the invent-tion is applied to the correction of misconvergence in a shadow mask tube.
Description
~6t~35~
EQUIPMENT TO CORRECT ~BERRATIONS OF A CATHOD~ RA~ BEAM
This invention relates to cathode-ray tube equipment including correction means for correcting aberrations of the cathode-ray beam as the beam is scanned across the screen.
Preferably the invention is applied to the correction of misconvergence in a shadow mask colour tube, hut it is also applicable to pin-cushion correction and dynamic focussing.
Such aberrations have in the past been corrected by manual adjustment of the cathode-ray tube analogue drive circuitry. British Patent 1,517,119 proposed that aberrations be corrected dynamically by reading correction signals from a digital store as the beam is being scanned across the screen. The correction signals are, however, directly representative of the corrections to be applied and this implementation is unduly expensive of storage space.
Our copending Canadian application 365,905, filed December
EQUIPMENT TO CORRECT ~BERRATIONS OF A CATHOD~ RA~ BEAM
This invention relates to cathode-ray tube equipment including correction means for correcting aberrations of the cathode-ray beam as the beam is scanned across the screen.
Preferably the invention is applied to the correction of misconvergence in a shadow mask colour tube, hut it is also applicable to pin-cushion correction and dynamic focussing.
Such aberrations have in the past been corrected by manual adjustment of the cathode-ray tube analogue drive circuitry. British Patent 1,517,119 proposed that aberrations be corrected dynamically by reading correction signals from a digital store as the beam is being scanned across the screen. The correction signals are, however, directly representative of the corrections to be applied and this implementation is unduly expensive of storage space.
Our copending Canadian application 365,905, filed December
2, 1980, proposes that the correction signals be derived from stored parameters and describes and claims analogue circuitry to achieve this end. Although this latter approach is a highly effective means for achieving correction, the reducing cost of digital circuitry makes the digital rather than the analogue approach an interesting alternative, especially if the digital circuitry can be kept ~ simple enough to occupy a single chip.
; 25 We have found that the key to achieving this simplicity is the calculus of finite differences in which the only operations required are those of signed additions and shift.
According to the invention, cathode-ray tube equipment including correction means for correcting aberrations of a cathode-ray beam as the beam is scanned across the screen, said correction means being responsive to correction signals, is characterised by a cligital store arranged in operation to UK9-79-00~
B~
1 store finite differences of functions defining the correction signals and digital calculating apparatus which in operation derives the correction signals by summing appropriate finite differences.
Preferably the cathode-ray tube is a shadow-mask colour tube and the aberration being corrected is misconvergence.
The invention will further be explained by way of example with reference to the drawings, in which:
Figure 1 is a diagram representing the screen of a cathode-ray tube;
Figure 2 is a schematic diagram of digital apparatus suitable for deriving functions from their finite differences;
Figure 3 is a schematic diagram of an al-ternative to that of Figure 2; and Figure 4 is a block diagram of a practical embodiment of digital calculating apparatus suitable for use in practising the invention.
We first explain the principles underlying the invention with reference to Figure 1. As is well known, the fact that the screen of a cathode-ray tube is not spherical with centre at the virtual source of an electron beam causes distortion of the lmage generated by the beam. The distortion, or non-linearity, of the image is a function of the beam position at the tube screen, so that the correction to be applied to the beam control circuitry is also a function of the notional beam position at the screen: F = F(x,y). In this discussion, x is the notional beam position measured parallel to the lines of a raster scan; _ is orthogonal to x. The non-linearity to be corrected may be beam focus or it may be pincushion distortion in a single gun tube. Of most interest is the correction of misconvergence in a multigun shadowmask cathode-ray tube. If the tube is of the well-known delta ~6~352 1 gun type with three electron guns arranged at the apices of the triangle, there are four correction signals to be gen-erated. These are the red, green, blue radial and blue latexal corrections. Each is a function of both x and _ and can be expressed as a polynomial. The invention proposes that as a rast~r image is being refreshed the correction function be digitally calculated from a small number of stored constants.
The raster consists of a sequence of parallel sequential horizontal sweeps 1 of the electron beams across the screen.
An image is displayed by selectively brightening the beams as they travel from left to right across the screen, the beams being blanked as they move from the right hand side of the screen to the beginning of the next line, i.e., during line flyback 2, and as they travel from the end of the bottom line to the beginning of the top line, i.e., during frame flyback (not shown). As the beams traverse one raster line 1, has a constant value and the correction signal calculation reduces to the evaluation of a polynomial in x only. In practice, the correction signals can be treated as constant for small ranges of x and there is no need to evaluate the function continuously. Each line of the raster is divided into equal zones 3 and the correction is calculated for each zone. Although application of the invention is not restricted to any specific range of orders of the polynomial function, satisfactory results have been obtained with F(x,y) as a cubic polynomial in _ and ~. By way of example, the evalua-tion of cubic polynomials will be described. It will be understood that there is an upper limit to the amount of computation that can be done as the CRT beam is moving across the screen. We have found however that computations involving quartics can satisfactorily be executed by the procedures we describe without delaying the tracing of the raster scan.
UK9-79-00~ -3-33S;~:
1 In a practical embodiment the CRT screen is divided into four quadrants I to IV with~different polynomials in each quadrant. In each quadrant there are 32 horizontal zones and 256 lines. In each zone a value of the polynomial corres-ponding to the coordinates of the zone is computed. The origin of the coordinate system is taken to be the top left-hand corner of each quadrant with x increasing from left to right and y increasing from top to bottom. Any cubic function of x and y can be written in the form F(x,y) = Ax3 + BX2 + Cx + D
where A, s, C and D are each cubic functions of _. For each line of the raster _ is constant. The computation of such functions over the four quadrants of a CRT screen, there being a different function for each quadrant, involves the following procedure:
1. Store the initial diEferences corresponding to the value of y for the top line of each quadrant.
2. As the CRT beam traverses the top line of the screen evaluate F for each zone 3, changing the function being eval-uated as the beam moves into the top right quadrant, lI~
; 25 We have found that the key to achieving this simplicity is the calculus of finite differences in which the only operations required are those of signed additions and shift.
According to the invention, cathode-ray tube equipment including correction means for correcting aberrations of a cathode-ray beam as the beam is scanned across the screen, said correction means being responsive to correction signals, is characterised by a cligital store arranged in operation to UK9-79-00~
B~
1 store finite differences of functions defining the correction signals and digital calculating apparatus which in operation derives the correction signals by summing appropriate finite differences.
Preferably the cathode-ray tube is a shadow-mask colour tube and the aberration being corrected is misconvergence.
The invention will further be explained by way of example with reference to the drawings, in which:
Figure 1 is a diagram representing the screen of a cathode-ray tube;
Figure 2 is a schematic diagram of digital apparatus suitable for deriving functions from their finite differences;
Figure 3 is a schematic diagram of an al-ternative to that of Figure 2; and Figure 4 is a block diagram of a practical embodiment of digital calculating apparatus suitable for use in practising the invention.
We first explain the principles underlying the invention with reference to Figure 1. As is well known, the fact that the screen of a cathode-ray tube is not spherical with centre at the virtual source of an electron beam causes distortion of the lmage generated by the beam. The distortion, or non-linearity, of the image is a function of the beam position at the tube screen, so that the correction to be applied to the beam control circuitry is also a function of the notional beam position at the screen: F = F(x,y). In this discussion, x is the notional beam position measured parallel to the lines of a raster scan; _ is orthogonal to x. The non-linearity to be corrected may be beam focus or it may be pincushion distortion in a single gun tube. Of most interest is the correction of misconvergence in a multigun shadowmask cathode-ray tube. If the tube is of the well-known delta ~6~352 1 gun type with three electron guns arranged at the apices of the triangle, there are four correction signals to be gen-erated. These are the red, green, blue radial and blue latexal corrections. Each is a function of both x and _ and can be expressed as a polynomial. The invention proposes that as a rast~r image is being refreshed the correction function be digitally calculated from a small number of stored constants.
The raster consists of a sequence of parallel sequential horizontal sweeps 1 of the electron beams across the screen.
An image is displayed by selectively brightening the beams as they travel from left to right across the screen, the beams being blanked as they move from the right hand side of the screen to the beginning of the next line, i.e., during line flyback 2, and as they travel from the end of the bottom line to the beginning of the top line, i.e., during frame flyback (not shown). As the beams traverse one raster line 1, has a constant value and the correction signal calculation reduces to the evaluation of a polynomial in x only. In practice, the correction signals can be treated as constant for small ranges of x and there is no need to evaluate the function continuously. Each line of the raster is divided into equal zones 3 and the correction is calculated for each zone. Although application of the invention is not restricted to any specific range of orders of the polynomial function, satisfactory results have been obtained with F(x,y) as a cubic polynomial in _ and ~. By way of example, the evalua-tion of cubic polynomials will be described. It will be understood that there is an upper limit to the amount of computation that can be done as the CRT beam is moving across the screen. We have found however that computations involving quartics can satisfactorily be executed by the procedures we describe without delaying the tracing of the raster scan.
UK9-79-00~ -3-33S;~:
1 In a practical embodiment the CRT screen is divided into four quadrants I to IV with~different polynomials in each quadrant. In each quadrant there are 32 horizontal zones and 256 lines. In each zone a value of the polynomial corres-ponding to the coordinates of the zone is computed. The origin of the coordinate system is taken to be the top left-hand corner of each quadrant with x increasing from left to right and y increasing from top to bottom. Any cubic function of x and y can be written in the form F(x,y) = Ax3 + BX2 + Cx + D
where A, s, C and D are each cubic functions of _. For each line of the raster _ is constant. The computation of such functions over the four quadrants of a CRT screen, there being a different function for each quadrant, involves the following procedure:
1. Store the initial diEferences corresponding to the value of y for the top line of each quadrant.
2. As the CRT beam traverses the top line of the screen evaluate F for each zone 3, changing the function being eval-uated as the beam moves into the top right quadrant, lI~
3. During line flyback compute the initial differencesfor the new value of _, i.e., the value of _ at the next raster line, for the top left and right quadrants, I, II, res-pectively.
4. Repeat for each line of the top half of the screen until the line flyback before the top raster line of the bottom quadrants, III, IV, when the initial diEferences corresponding for the functions for the bottom quadrants, III, IVI are retrieved.
5. Repeat for the bottom quadrants.
rrhe polynomial function of x and _ is evaluated using finite differences. Consider the function:
UK9-79-00~
~ ~ 6~ 3 1 F(x) = Ax3 -~ Bx2 + Cx ~ D
Evaluate it at x = 0, 1, 2, 3, 4, and take the differences:
x = 0 1 2 3 4 F(x) = D A+B+C+D 8A+4B+2C+D 27A+9B~3C+D 64A+16B+4C+D
dl = A+B+C 7A~3B+C l9A+5s*c 37A+7B+C
d2 = 6A+2B 12A+2B 18A+2B
d3 = 6A 6A
It can be seen that the third differences d3 all have the value 6A. In general a polynomlal of degree N has constant value Nth order differences with all higher order differences zero- Given F(O), -11~ d21 and d3, the values of F(xi) (i = 1, 2, 3, 4, ....), with the intervals (xn, xn~l) equal, can be found by addition.
Apparatus for calculating the function F(xi) is schematic-ally illustrated at Figure 2 which shows a first-in first-out store FIFO, two registers P and Q, an adder A and an output register O/R. A first-in first-out store is a store from which data is retrieved only in the order in which it was entered in the store. The output of FIFO is connected -to registers P and Q which are connected to adder A. The output of adder A is connected~as input to FIFO and to the output ~reglster O/R. Initially FIFO stores, FtXl)~ dll, d21 and _3 in that order, with F(xl) occupying the location nearest the output. The following table specifies the procedure whereby (x2), dl2 and d22 are calculated ~6~3~2 Operations Content/of: P Q PIFO
1. Read FIFO to P F(xl) 2. Read FIFO to Q -11 3. Sum P,Q to FIFO and O/R F(xl)+_ll F(X2) 4. Read FIFO to P -21 5. Sum P,Q to FIFO -11 -21 -12
rrhe polynomial function of x and _ is evaluated using finite differences. Consider the function:
UK9-79-00~
~ ~ 6~ 3 1 F(x) = Ax3 -~ Bx2 + Cx ~ D
Evaluate it at x = 0, 1, 2, 3, 4, and take the differences:
x = 0 1 2 3 4 F(x) = D A+B+C+D 8A+4B+2C+D 27A+9B~3C+D 64A+16B+4C+D
dl = A+B+C 7A~3B+C l9A+5s*c 37A+7B+C
d2 = 6A+2B 12A+2B 18A+2B
d3 = 6A 6A
It can be seen that the third differences d3 all have the value 6A. In general a polynomlal of degree N has constant value Nth order differences with all higher order differences zero- Given F(O), -11~ d21 and d3, the values of F(xi) (i = 1, 2, 3, 4, ....), with the intervals (xn, xn~l) equal, can be found by addition.
Apparatus for calculating the function F(xi) is schematic-ally illustrated at Figure 2 which shows a first-in first-out store FIFO, two registers P and Q, an adder A and an output register O/R. A first-in first-out store is a store from which data is retrieved only in the order in which it was entered in the store. The output of FIFO is connected -to registers P and Q which are connected to adder A. The output of adder A is connected~as input to FIFO and to the output ~reglster O/R. Initially FIFO stores, FtXl)~ dll, d21 and _3 in that order, with F(xl) occupying the location nearest the output. The following table specifies the procedure whereby (x2), dl2 and d22 are calculated ~6~3~2 Operations Content/of: P Q PIFO
1. Read FIFO to P F(xl) 2. Read FIFO to Q -11 3. Sum P,Q to FIFO and O/R F(xl)+_ll F(X2) 4. Read FIFO to P -21 5. Sum P,Q to FIFO -11 -21 -12
6. Read FIFO to Q d3
7. Sum P,Q to FIFO -21 d3 d22
8. Clear P 0
9. Sum P,Q to FIFO d3 The operation specified by the third line of the table makes the function F available at the output register O/R. The remaining operations obtain the differences and load them into FIFO in the correct order.
An alternative arrangement is shown in Figure 3 in which the FIFO is a four stage shift register connected so that the two right-most stages can be read in parallel to the adder A, the second stage being connected to the adder through a zeroising circuit Z. Initially the FIFO holds the values, reading from right to left, F(xl), -11' d21 and d3- The following table illustrates that the arrangement of Figure 3 efficiently calculates the required finite differences:
Ope~ration FIFO ~ontent F(xl),_ll~ d21' 3 1. Sum to O/R and FIFO -11' d21' d3~ F(X2) 2. Sum to FIFO -21' -3' F(X2)' dl2 3. Sum to FIFO d3, F~X2), dl2, d22 Activate zeroising circuit and 4. Sum to FIFO F(x2)~ -12' -22' -3 3S;2 1 Essentially the process ls the four-fold repetition of the same operation with the gates to O/R being opened on the first operation and the zeroising circuit being activated on the last operation. This can be more readily incorporated in a microcircuit module than the slightly more complex arrange-ment of Eigure 2 and Table 1.
Before describing a practical implementation of the idealized apparatus of Fiyures 2 and 3 it is necessary to consider the errors arising out of the use of finite differences. Errors arise due both to errors in the initial values of the differences from which all differences are derived and due to truncation errors occuring in the course of summing the differences. The following discussion is restricted to cubic functions and for convenience the function F(xn) will be called dOn. The binary word representing ea--h difference may be envisaged as divided into integer and fraction parts by a notional "binary point". It will be assumed, without loss of generality, that the integer part of don is the required result of a finite difference summation and that it is required to confine errors to the fraction part. The stored initial values doo, dlo, d20 and d30 are only approximations to the actual values d, of these differences ("actual" meaning "expxessed to such degree of accuracy that errors arising in truncation-free caIcula-tion are in practice negliga~le"). Suppose:
doo doo + Eo ~0 dlo + El d20 E2 d30 d30 + E3 It can be shown that the error E in calculating ~ n where _ is larger is E = (approx.) Eo + nEl + (n /2)E2 + (n /6)E3 ~Ld~.~ 3~
1 This means that higher order differences must be stored with higher precision. But:since higher order differences are smaller than the low order differences it is possible to assign more orders of their numerical representation to the fractional part of their value. Accordingly, the same number of binary integers are assigned to each orde.r of difference but the number of places assigned to the fractional part of each difference is progressively increased for higher order differences. An equal shift of the binary point for each difference order is the easiest to implement and has been found to give satisfactory results. The length of the shift is log2(n/2) bits, rounded to the next largest integer.
The other source of error results from the above shift-ing scheme and is due to truncation when differences with the binary point in different positions are added together. The preferred way of compensating for truncation errors is to add as a carry~in to the lowest order of the number with the smaller number of fractional orders the most significant truncated bit from the other number. For example do 1 1 0 1 1 0 . 1 --1 1 0 1 0 1 . 1 1 0 1 Truncation occurs at the first binary fraction order. The 1 in the second binary fraction order is added to the sum.
This reduces the maximum truncation error to the value of the highest truncated order. The truncation error can be regarded as an initialization error in the next lower order difference. Therefore, difference _ must have as many fraction places as are required to compensate for initialization error in differences m + 1. Since, as already explained, each difference needs approximately log2(n/2) more fractional orders than the next higher order, the number of fractional places becomes:
UK9-79-00~ -8-3;,æ
do = log2 dl = log2 (n /2 d2 = log2 (n3/4) d3log2 (n4/8) The expression for d3 is a simplification since there is, in the case being considered, no d4. If n = 2q, the number of fractional orders are:
do q -1 = 2q - 1 d2 = 3q - 2 d3 = 4q ~ 3 We next consider the range of values of the differences.
It can be shown that the cubic function y = x (4x-3) : where both and y take any values in the interval (0,1) including the end points .is the function with maximum first, second and third order differentials. Consldering this ;~ function to be multiplied by 2P, it can be shown that, if :
the result lS to be computed to a precision of p bits, then dl must have p+4-q integer bits + sign d2 must have p+6-2q integer bits ~ sign : d3 must have p+7-3q integer bits + sign Summing the integer and fractional parts ana adding one bit for the sign, the total number of bits required for each difference is as follows:
-0 = P+q dl = p+4+q d2 = p+5~q _3 = P~5+q The total numhers of bits of each difference which must be correctly initialized are:
~G~335~
do dl = p+5 d2 = p+6 -3 p+6 Figure 4 shows a practical embodiment of the invention.
The embodiment includes a random access store 10, an adder 2Q, a shift register 30, an output register 40 and a di~ital-to-analogue converter 50. The store 10 replaces the function of the first-in first-out store shGwn in Figures 2 and 3 and has an input port 11, output port 12 and address port 13.
The output register 12 is connected to input port 21 of the adder 20. Another input to the adder 20 is pro~ided at port 22. The output of adder 20 is supplied to the parallel inputs 31 of shift register 30. The parallel outputs are connected to a register 40, to the input port 11 of store 10, and to a 2-bit arithmetic right shift device 23. One output of the shift device 23 is connected to port 22 and another output 24 provides a carry-in to the lowest order of the adder 20. Shift register 30 has a single-bit input 33 for the supply of data from an external source. This is the means whereby initialization data is made available to the store 10.
The connections shown in Figure 4 are representative, except for input 33, of a plurality of bit lines. On the basis of the theory outlined above, if it is required ko provide an accurate 8-bit output for 32 horizontal zones (values of F(x,y) with _ constant) in each quadrant, we have p = 8, n = 32 = 2q, and so q = 5. The largest number of bits in the initialized values is 14 (for d2 and d3). The _ computation must provide an accurate 14 bit result for 256 lines. It follows that p = 14 and q -- 8 giving a highes-t number of total bits as 27 (for d2 and 3~. ~ d~ta flow of 28 bits wide is an appropriate size. Port 22 is 26 bits -~L6~3~2 1 so that as already explained the ~inary points are aligned -and register 40 is 8 bits to take the result which occupies bits 10 to 17 of the output of register 30 (most significant bit is bit 0).
We now describe the information held in the store 10.
The notation used for the addresses is hexadecimal, i.e. the addresses run from 00, which is binary 0000 0000, to FF, which is binary 1111 1111. By way of example, it is assumed that each frame of the image is displayed as two interlaced fields, field 1 and field 2, as is common in television practice.
Storage liocations Contents 00 to 03 d3L to dOL respectively - horizontal zone work store, left half of screen, quadrant I or III as appropriate, field 1.
An alternative arrangement is shown in Figure 3 in which the FIFO is a four stage shift register connected so that the two right-most stages can be read in parallel to the adder A, the second stage being connected to the adder through a zeroising circuit Z. Initially the FIFO holds the values, reading from right to left, F(xl), -11' d21 and d3- The following table illustrates that the arrangement of Figure 3 efficiently calculates the required finite differences:
Ope~ration FIFO ~ontent F(xl),_ll~ d21' 3 1. Sum to O/R and FIFO -11' d21' d3~ F(X2) 2. Sum to FIFO -21' -3' F(X2)' dl2 3. Sum to FIFO d3, F~X2), dl2, d22 Activate zeroising circuit and 4. Sum to FIFO F(x2)~ -12' -22' -3 3S;2 1 Essentially the process ls the four-fold repetition of the same operation with the gates to O/R being opened on the first operation and the zeroising circuit being activated on the last operation. This can be more readily incorporated in a microcircuit module than the slightly more complex arrange-ment of Eigure 2 and Table 1.
Before describing a practical implementation of the idealized apparatus of Fiyures 2 and 3 it is necessary to consider the errors arising out of the use of finite differences. Errors arise due both to errors in the initial values of the differences from which all differences are derived and due to truncation errors occuring in the course of summing the differences. The following discussion is restricted to cubic functions and for convenience the function F(xn) will be called dOn. The binary word representing ea--h difference may be envisaged as divided into integer and fraction parts by a notional "binary point". It will be assumed, without loss of generality, that the integer part of don is the required result of a finite difference summation and that it is required to confine errors to the fraction part. The stored initial values doo, dlo, d20 and d30 are only approximations to the actual values d, of these differences ("actual" meaning "expxessed to such degree of accuracy that errors arising in truncation-free caIcula-tion are in practice negliga~le"). Suppose:
doo doo + Eo ~0 dlo + El d20 E2 d30 d30 + E3 It can be shown that the error E in calculating ~ n where _ is larger is E = (approx.) Eo + nEl + (n /2)E2 + (n /6)E3 ~Ld~.~ 3~
1 This means that higher order differences must be stored with higher precision. But:since higher order differences are smaller than the low order differences it is possible to assign more orders of their numerical representation to the fractional part of their value. Accordingly, the same number of binary integers are assigned to each orde.r of difference but the number of places assigned to the fractional part of each difference is progressively increased for higher order differences. An equal shift of the binary point for each difference order is the easiest to implement and has been found to give satisfactory results. The length of the shift is log2(n/2) bits, rounded to the next largest integer.
The other source of error results from the above shift-ing scheme and is due to truncation when differences with the binary point in different positions are added together. The preferred way of compensating for truncation errors is to add as a carry~in to the lowest order of the number with the smaller number of fractional orders the most significant truncated bit from the other number. For example do 1 1 0 1 1 0 . 1 --1 1 0 1 0 1 . 1 1 0 1 Truncation occurs at the first binary fraction order. The 1 in the second binary fraction order is added to the sum.
This reduces the maximum truncation error to the value of the highest truncated order. The truncation error can be regarded as an initialization error in the next lower order difference. Therefore, difference _ must have as many fraction places as are required to compensate for initialization error in differences m + 1. Since, as already explained, each difference needs approximately log2(n/2) more fractional orders than the next higher order, the number of fractional places becomes:
UK9-79-00~ -8-3;,æ
do = log2 dl = log2 (n /2 d2 = log2 (n3/4) d3log2 (n4/8) The expression for d3 is a simplification since there is, in the case being considered, no d4. If n = 2q, the number of fractional orders are:
do q -1 = 2q - 1 d2 = 3q - 2 d3 = 4q ~ 3 We next consider the range of values of the differences.
It can be shown that the cubic function y = x (4x-3) : where both and y take any values in the interval (0,1) including the end points .is the function with maximum first, second and third order differentials. Consldering this ;~ function to be multiplied by 2P, it can be shown that, if :
the result lS to be computed to a precision of p bits, then dl must have p+4-q integer bits + sign d2 must have p+6-2q integer bits ~ sign : d3 must have p+7-3q integer bits + sign Summing the integer and fractional parts ana adding one bit for the sign, the total number of bits required for each difference is as follows:
-0 = P+q dl = p+4+q d2 = p+5~q _3 = P~5+q The total numhers of bits of each difference which must be correctly initialized are:
~G~335~
do dl = p+5 d2 = p+6 -3 p+6 Figure 4 shows a practical embodiment of the invention.
The embodiment includes a random access store 10, an adder 2Q, a shift register 30, an output register 40 and a di~ital-to-analogue converter 50. The store 10 replaces the function of the first-in first-out store shGwn in Figures 2 and 3 and has an input port 11, output port 12 and address port 13.
The output register 12 is connected to input port 21 of the adder 20. Another input to the adder 20 is pro~ided at port 22. The output of adder 20 is supplied to the parallel inputs 31 of shift register 30. The parallel outputs are connected to a register 40, to the input port 11 of store 10, and to a 2-bit arithmetic right shift device 23. One output of the shift device 23 is connected to port 22 and another output 24 provides a carry-in to the lowest order of the adder 20. Shift register 30 has a single-bit input 33 for the supply of data from an external source. This is the means whereby initialization data is made available to the store 10.
The connections shown in Figure 4 are representative, except for input 33, of a plurality of bit lines. On the basis of the theory outlined above, if it is required ko provide an accurate 8-bit output for 32 horizontal zones (values of F(x,y) with _ constant) in each quadrant, we have p = 8, n = 32 = 2q, and so q = 5. The largest number of bits in the initialized values is 14 (for d2 and d3). The _ computation must provide an accurate 14 bit result for 256 lines. It follows that p = 14 and q -- 8 giving a highes-t number of total bits as 27 (for d2 and 3~. ~ d~ta flow of 28 bits wide is an appropriate size. Port 22 is 26 bits -~L6~3~2 1 so that as already explained the ~inary points are aligned -and register 40 is 8 bits to take the result which occupies bits 10 to 17 of the output of register 30 (most significant bit is bit 0).
We now describe the information held in the store 10.
The notation used for the addresses is hexadecimal, i.e. the addresses run from 00, which is binary 0000 0000, to FF, which is binary 1111 1111. By way of example, it is assumed that each frame of the image is displayed as two interlaced fields, field 1 and field 2, as is common in television practice.
Storage liocations Contents 00 to 03 d3L to dOL respectively - horizontal zone work store, left half of screen, quadrant I or III as appropriate, field 1.
10 to 13 d3R to dOR respectively - horizontal zone work store, right half of screen, quadrant II or IV as appropriate, field 1.
20 to 23 3( 30L~ to d0(d3oL~ respectively _ work s-torage for the computation of the initial value, d30L, field 1.
24 to 27 3( 20L) to d0(d2oL) - work storage for the computation of the initial value, d20L, ~ield 1.
28 to 2B 3(dl0L) to do~dlOL) - work storage for the computation of the initial value, d~o~r field 1.
~6~33;~
1 TABLE_3 _Cont'd~
Storage Locations Contents . . _ 2C to 2F 3( OOL) to d0(dooL~ - work storage for the computation of the initial , dooL, field 1.
30 to 3F 3( 30R) to d0(dooR) - work storage for the computation of the values of 30R' d20R' dloR and dooR, field 1 : (arranged in the same way as addresses addresses 20 - 2F).
40 to 5F Initial values of the differences of which later values are computed by using work storage 20 to 3F, upper part of screen, field 1 (arranged in the same way as addresses 20 - 3F).
60 to 7F Initial values of the differences of which later values are computed by using work storage 20 to 3F, lower part of screen, field 1 (arranged in the same wa~ as addresses 20 - 3F).
80 to 83 These locations contain the differences 90 to 93 for ~ield 2, arranged in the same AO to AF fashion as the differences for field 1.
BO to BF
CO to DF
E0 to FF
With the differences stored as in Table 3, the operation sequences set out below as Table 4 are executed.
: 30 i~.~6633;:~%
Operation Sequence -1) Horizontal zone (4 cycles) clear,read F 0 0 X 0 0 0 0 write " d3 read F 0 0 X 0 0 0 1 write d2 read F 0 0 X 0 0 1 0 write dl I0 read F 0 0 X 0 0 1 1 set output,write " do 2) Left-most & middle hori`zontal zones (4 cycles) clear,read F 0 1 X 0 0 1 1 d3 write F 0 0 X 0 0 0 0 (clear),read F 0 1 X 0 1 1 1 d2 write F 0 0 X 0 0 0 1 (clear),read F 0 1 X 1 0 1 1 d write F 0 0 X 0 0 1 0 (clear),read F 0 1 X 1 1 1 1 _0 set output,write F 0 0 X 0 0 1 1 (clear) only performed on middle zone ~l~L6(~3~2 1 TABLE 4 (Cont'd) 3) 1ine flyback (32 cycles) clear,read F 0 1 0 d3~d30L) write "
read F 0 l 0 0 0 0 1 d2(d30L) write "
read F 0 1 1 1 1 l dl(dooR) write "
read F 0 l l l l l l _o(dooR) write "
set output performed while writing -0(-OOL) clear shift register is activated while reading any 3 4) 1st or middle line flyback (32 cycles) clear,read F l Y 0 d3(d30L) write F 0 1 0 0 0 0 0 clear,read F 1 Y 0 0 0 0 l _2(d30L) write F 0 l 0 0 0 0 1 -.
clear,read F l Y l l l 1 -l(-OOR) write F 0 l 1 1 1 l 0 clear,read F l Y l l l l l 'do(dOOR) write F 0 l l l l l l set output performed while writing~do(dOOL) clear shift register is activated on all read operations F = Field #, Y = upper/lower, X = left/right ~ 51 6~3;~2 1 The circuitry operates cyclicallyt each cycle beginning with a read from the store, and after a pause to permit the result of the consequent addition to be entered in the shift register, the result is written back into the store at the same or a different location. If it is required to shift the contents of the shift register to align binary points this is done as the store is being read.
The most frequently performed operation sequence is that given in section 1 of Table 4. On the first cycle the differ-ence _3, a constant, is copied from working storage into register 30. In the second cycle the difference d2n is added to d3 to get -2(n+1) which is written in working storage in preparation for the next operation sequence. The third cycle -ln to d2(n+1) to get -l(n+l) and the fourth cycle adds -On to -l(n~l) to get do(n+l). This is the required correc-tion value and, as well as being written into working store, is provided at the output register. It will now be noted that the variables F and X cause selection of the appropriate working storage section of the random access store in accord-ance with whether field 1 or 2 and a left or right half of the screen is being processed, for example F = 0, X = 0 cause the operation sequence to access locations 00 to 03.
The clear operation performed on the first cycle zeroizes the contents of register 30. Operation 1 is modified as shown in sequence 2 at the left-most zone, the first zone at the beginning of each line of a quadrant. Although the dol, dll, d21 and d3 are calculated in the same way as during sequence 1 the initial values, do~ d2 and d3, are taken from that part of the random access store in which they were written during line flyback. For example, for the top left quadrant the values are read flom locations 23, 27 2B and 2F.
~.~G6~3~2 1 During a line flyback which is not before the top line of a quadrant, operation sequence 3 is used. It consists of 32 cycles, eight groups of four cycles during which the values of the initial differences are computed for the left and the right quadrants. On field 1, the first four cycles access locations 20 to 23, the next four access locakions 2~
to 27 and so on, until the last four cycles access locations 3C to 3F (see Table 3). Each group of four cycles computes one of the differences _3 to _0 for one of the quadrants, for example the differenCes do(dooR)~ dl(d00R)' d2(d00R) d3(dooR) for the lowest order difference in the left quadrantt which is used in operation sequence 2. For the flyback before the first line of a quadrant, operating sequence 4 is used, during which the initial values of the differences are trans-ferred from, in the case of field 1, locations 40 to 5F or 60 to 7F, depending on whether the flyback is before the top or bottom halves of the screen. Although the initial values pass through adder 20 the clearing of register 30 ensures that the other addend is zero.
There has been described digital apparatus for use in providing correction signals to control a cathode-ray tube, the correction signals being calculated from stored para meters by the use of finite differences as the cathode-ray beam is tracing a raster.
20 to 23 3( 30L~ to d0(d3oL~ respectively _ work s-torage for the computation of the initial value, d30L, field 1.
24 to 27 3( 20L) to d0(d2oL) - work storage for the computation of the initial value, d20L, ~ield 1.
28 to 2B 3(dl0L) to do~dlOL) - work storage for the computation of the initial value, d~o~r field 1.
~6~33;~
1 TABLE_3 _Cont'd~
Storage Locations Contents . . _ 2C to 2F 3( OOL) to d0(dooL~ - work storage for the computation of the initial , dooL, field 1.
30 to 3F 3( 30R) to d0(dooR) - work storage for the computation of the values of 30R' d20R' dloR and dooR, field 1 : (arranged in the same way as addresses addresses 20 - 2F).
40 to 5F Initial values of the differences of which later values are computed by using work storage 20 to 3F, upper part of screen, field 1 (arranged in the same way as addresses 20 - 3F).
60 to 7F Initial values of the differences of which later values are computed by using work storage 20 to 3F, lower part of screen, field 1 (arranged in the same wa~ as addresses 20 - 3F).
80 to 83 These locations contain the differences 90 to 93 for ~ield 2, arranged in the same AO to AF fashion as the differences for field 1.
BO to BF
CO to DF
E0 to FF
With the differences stored as in Table 3, the operation sequences set out below as Table 4 are executed.
: 30 i~.~6633;:~%
Operation Sequence -1) Horizontal zone (4 cycles) clear,read F 0 0 X 0 0 0 0 write " d3 read F 0 0 X 0 0 0 1 write d2 read F 0 0 X 0 0 1 0 write dl I0 read F 0 0 X 0 0 1 1 set output,write " do 2) Left-most & middle hori`zontal zones (4 cycles) clear,read F 0 1 X 0 0 1 1 d3 write F 0 0 X 0 0 0 0 (clear),read F 0 1 X 0 1 1 1 d2 write F 0 0 X 0 0 0 1 (clear),read F 0 1 X 1 0 1 1 d write F 0 0 X 0 0 1 0 (clear),read F 0 1 X 1 1 1 1 _0 set output,write F 0 0 X 0 0 1 1 (clear) only performed on middle zone ~l~L6(~3~2 1 TABLE 4 (Cont'd) 3) 1ine flyback (32 cycles) clear,read F 0 1 0 d3~d30L) write "
read F 0 l 0 0 0 0 1 d2(d30L) write "
read F 0 1 1 1 1 l dl(dooR) write "
read F 0 l l l l l l _o(dooR) write "
set output performed while writing -0(-OOL) clear shift register is activated while reading any 3 4) 1st or middle line flyback (32 cycles) clear,read F l Y 0 d3(d30L) write F 0 1 0 0 0 0 0 clear,read F 1 Y 0 0 0 0 l _2(d30L) write F 0 l 0 0 0 0 1 -.
clear,read F l Y l l l 1 -l(-OOR) write F 0 l 1 1 1 l 0 clear,read F l Y l l l l l 'do(dOOR) write F 0 l l l l l l set output performed while writing~do(dOOL) clear shift register is activated on all read operations F = Field #, Y = upper/lower, X = left/right ~ 51 6~3;~2 1 The circuitry operates cyclicallyt each cycle beginning with a read from the store, and after a pause to permit the result of the consequent addition to be entered in the shift register, the result is written back into the store at the same or a different location. If it is required to shift the contents of the shift register to align binary points this is done as the store is being read.
The most frequently performed operation sequence is that given in section 1 of Table 4. On the first cycle the differ-ence _3, a constant, is copied from working storage into register 30. In the second cycle the difference d2n is added to d3 to get -2(n+1) which is written in working storage in preparation for the next operation sequence. The third cycle -ln to d2(n+1) to get -l(n+l) and the fourth cycle adds -On to -l(n~l) to get do(n+l). This is the required correc-tion value and, as well as being written into working store, is provided at the output register. It will now be noted that the variables F and X cause selection of the appropriate working storage section of the random access store in accord-ance with whether field 1 or 2 and a left or right half of the screen is being processed, for example F = 0, X = 0 cause the operation sequence to access locations 00 to 03.
The clear operation performed on the first cycle zeroizes the contents of register 30. Operation 1 is modified as shown in sequence 2 at the left-most zone, the first zone at the beginning of each line of a quadrant. Although the dol, dll, d21 and d3 are calculated in the same way as during sequence 1 the initial values, do~ d2 and d3, are taken from that part of the random access store in which they were written during line flyback. For example, for the top left quadrant the values are read flom locations 23, 27 2B and 2F.
~.~G6~3~2 1 During a line flyback which is not before the top line of a quadrant, operation sequence 3 is used. It consists of 32 cycles, eight groups of four cycles during which the values of the initial differences are computed for the left and the right quadrants. On field 1, the first four cycles access locations 20 to 23, the next four access locakions 2~
to 27 and so on, until the last four cycles access locations 3C to 3F (see Table 3). Each group of four cycles computes one of the differences _3 to _0 for one of the quadrants, for example the differenCes do(dooR)~ dl(d00R)' d2(d00R) d3(dooR) for the lowest order difference in the left quadrantt which is used in operation sequence 2. For the flyback before the first line of a quadrant, operating sequence 4 is used, during which the initial values of the differences are trans-ferred from, in the case of field 1, locations 40 to 5F or 60 to 7F, depending on whether the flyback is before the top or bottom halves of the screen. Although the initial values pass through adder 20 the clearing of register 30 ensures that the other addend is zero.
There has been described digital apparatus for use in providing correction signals to control a cathode-ray tube, the correction signals being calculated from stored para meters by the use of finite differences as the cathode-ray beam is tracing a raster.
Claims (5)
1. Cathode ray tube equipment including correction means for correcting an aberration of a cathode ray beam as the beam is scanned across the screen, said correction means being responsive to correction signals, characterized by a digital store arranged in operation to store finite differences of functions defining the correction signals and digital calculating apparatus which in operation derives cyclicy, successive correction signals by summing appropriate finite differences.
2. Equipment as claimed in claim 1, in which the cathode ray tube is a shadow mask colour tube, the aberration being corrected is misconvergence, and the tube is provided with convergence correction coils, wherein a digital-to-analogue conversion means converts the correction signals to correction currents which are supplied to the convergence correction coils.
3. Equipment as claimed in claim 1 or 2, wherein the digital calculating apparatus includes an adder and a register, the output of the digital store being connected to the input of the adder, the output of the adder being connected to the input of the register, the output of the register being connected to the input of the digital store and to another input of the adder through a shift device which imposes a shift on data being transferred from the register to the said another input of the adder so as to provide reduction of error by shifting higher order differences relative to lower order differences before addition.
4. Equipment as claimed in claim 2 wherein the digital store is arranged in operation to store digital values which are the initial differences of polynomial correction functions, said values being altered iteratively by the digital calculating apparatus and the results being returned to said store to be read therefrom to perform succeeding calculations.
5. Equipment as claimed in claim 4 wherein the digital calculating apparatus includes an adder and a register, the output of the digital store being connected to the input of the adder, the output of the adder being connected to the input of the register, the output of the register being connected to the input of the digital store and to another input of the adder through a shift device which imposes a shift on data being transferred from the register to the said another input of the adder so as to provide reduction of error by shifting higher order differences relative to lower order differences before addition.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| GB7943294 | 1979-12-15 | ||
| GB7943294A GB2066029B (en) | 1979-12-15 | 1979-12-15 | Digitally stored differences for correction of crt aberrations |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1160352A true CA1160352A (en) | 1984-01-10 |
Family
ID=10509881
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA000364796A Expired CA1160352A (en) | 1979-12-15 | 1980-11-17 | Equipment to correct aberrations of a cathode-ray beam |
Country Status (6)
| Country | Link |
|---|---|
| US (1) | US4354143A (en) |
| EP (1) | EP0030603B1 (en) |
| JP (1) | JPS5694892A (en) |
| CA (1) | CA1160352A (en) |
| DE (1) | DE3065630D1 (en) |
| GB (1) | GB2066029B (en) |
Families Citing this family (16)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| NL8005186A (en) * | 1980-09-17 | 1982-04-16 | Koninkl Philips Electronics Nv | TELEVISION CIRCUIT FOR APPLICATION IN SIGNAL RECORDING RESPECTIVE DISPLAY. |
| US4749918A (en) * | 1981-12-08 | 1988-06-07 | Rca Licensing Corporation | System for correcting for color impurities due to horizontal beam landing errors in flat panel display devices |
| GB2132057B (en) * | 1982-09-09 | 1986-04-23 | Link Electronics Ltd | Electro-optical image correction |
| GB2126855B (en) * | 1982-09-09 | 1986-04-23 | Link Electronics Ltd | Focus correction |
| JPS60236380A (en) * | 1984-05-09 | 1985-11-25 | Hitachi Ltd | Focus correcting device of cathode-ray tube |
| EP0162123B2 (en) * | 1984-05-23 | 1992-03-04 | Deutsche ITT Industries GmbH | Method and circuit arrangement for digital deflection correction of television picture tubes |
| JPS61140669U (en) * | 1985-02-20 | 1986-08-30 | ||
| JPS61140670U (en) * | 1985-02-20 | 1986-08-30 | ||
| US4680510A (en) * | 1985-04-12 | 1987-07-14 | Hazeltine Corporation | Color monitor with improved synchronization |
| US4757239A (en) * | 1985-10-18 | 1988-07-12 | Hilliard-Lyons Patent Management, Inc. | CRT display system with automatic alignment employing personality memory |
| US4835602A (en) * | 1987-08-27 | 1989-05-30 | North American Philips Corporation | Color projection television system with apparatus for correcting misconvergence and misgeometry which calculates coefficients of equations representing deflection correction waveforms |
| DE4109856A1 (en) * | 1991-03-26 | 1992-10-01 | Thomson Brandt Gmbh | TV receiver colour CRT with horizontal colour strips - uses index strips to provide correction values for electron beam position entered in digital memory |
| US5274307A (en) * | 1991-08-15 | 1993-12-28 | Zenith Electronics Corporation | Single IC for CRT display control waveform generation |
| DE4139129A1 (en) * | 1991-11-28 | 1993-06-09 | Deutsche Thomson-Brandt Gmbh, 7730 Villingen-Schwenningen, De | TELEVISION TELEVISION |
| EP0835583B1 (en) * | 1996-04-26 | 2002-01-09 | Koninklijke Philips Electronics N.V. | Spline waveform generation |
| KR100393559B1 (en) * | 2000-09-30 | 2003-08-02 | 삼성전기주식회사 | Control method for digital dynamic convergence and system for the same |
Family Cites Families (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US3942067A (en) * | 1974-06-21 | 1976-03-02 | General Electric Company | Multi-gun cathode ray tube convergence system |
| GB1517119A (en) * | 1976-12-22 | 1978-07-12 | Ibm | Cathode ray tube control apparatus |
| GB1586201A (en) * | 1977-09-15 | 1981-03-18 | Ibm | Methods of generating correction factor signals for cathode ray tubes |
-
1979
- 1979-12-15 GB GB7943294A patent/GB2066029B/en not_active Expired
-
1980
- 1980-10-23 DE DE8080106473T patent/DE3065630D1/en not_active Expired
- 1980-10-23 EP EP80106473A patent/EP0030603B1/en not_active Expired
- 1980-11-17 CA CA000364796A patent/CA1160352A/en not_active Expired
- 1980-12-01 JP JP16814980A patent/JPS5694892A/en active Granted
- 1980-12-08 US US06/214,146 patent/US4354143A/en not_active Expired - Lifetime
Also Published As
| Publication number | Publication date |
|---|---|
| GB2066029B (en) | 1983-03-23 |
| EP0030603A1 (en) | 1981-06-24 |
| GB2066029A (en) | 1981-07-01 |
| JPS5694892A (en) | 1981-07-31 |
| EP0030603B1 (en) | 1983-11-16 |
| JPS6235312B2 (en) | 1987-07-31 |
| DE3065630D1 (en) | 1983-12-22 |
| US4354143A (en) | 1982-10-12 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CA1160352A (en) | Equipment to correct aberrations of a cathode-ray beam | |
| US4203054A (en) | Correction factor signals for cathode ray tubes | |
| US4672275A (en) | Digital process and apparatus for convergence correction having adjustment points and correction portions determined by the adjustment point selected | |
| US5027287A (en) | Device for the digital processing of images to obtain special geometrical effects | |
| US4236174A (en) | Color correction of image display | |
| US4630039A (en) | Display processing apparatus | |
| US5506481A (en) | Registration error correction device | |
| DK147030B (en) | Cathode ray tube control apparatus with distortion correction device | |
| GB2172167A (en) | Video signal processing | |
| EP0264961A2 (en) | Television special effects system | |
| GB2150797A (en) | Graphic display system | |
| EP0068130B1 (en) | Display system and method of forming displays | |
| US4441057A (en) | Correction apparatus for a cathode ray tube | |
| EP0509043B1 (en) | Improvements in and relating to the production of digital video effects | |
| US5220428A (en) | Digital video effects apparatus for image transposition | |
| KR100189908B1 (en) | Color correction apparatus & method therefor using two-dimensional chromaticity partitioning | |
| US5315540A (en) | Method and hardware for dividing binary signal by non-binary integer number | |
| US4442545A (en) | Compaction of television display graphics in phantom-raster-scanned image memory | |
| EP0268359B1 (en) | Method and apparatus for processing video image signals | |
| US3809948A (en) | Display systems | |
| EP0429563B1 (en) | Digital convergence system | |
| JP2647073B2 (en) | Graphic display device | |
| JPH05227536A (en) | Digital convergence device | |
| US5065076A (en) | Digital convergence system | |
| SU788434A1 (en) | Device for correcting for main types of deflection aberrations |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| MKEX | Expiry |